<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Implementation and Accuracy</title>
<link rel="stylesheet" href="../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Math Toolkit 3.3.0">
<link rel="up" href="../inverse_complex.html" title="Chapter 15. Complex Number Functions">
<link rel="prev" href="../inverse_complex.html" title="Chapter 15. Complex Number Functions">
<link rel="next" href="asin.html" title="asin">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
<td align="center"><a href="../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../inverse_complex.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inverse_complex.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="asin.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.complex_implementation"></a><a class="link" href="complex_implementation.html" title="Implementation and Accuracy">Implementation and
    Accuracy</a>
</h2></div></div></div>
<p>
      Although there are deceptively simple formulae available for all of these functions,
      a naive implementation that used these formulae would fail catastrophically
      for some input values. The Boost versions of these functions have been implemented
      using the methodology described in "Implementing the Complex Arcsine and
      Arccosine Functions Using Exception Handling" by T. E. Hull Thomas F.
      Fairgrieve and Ping Tak Peter Tang, ACM Transactions on Mathematical Software,
      Vol. 23, No. 3, September 1997. This means that the functions are well defined
      over the entire complex number range, and produce accurate values even at the
      extremes of that range, where as a naive formula would cause overflow or underflow
      to occur during the calculation, even though the result is actually a representable
      value. The maximum theoretical relative error for all of these functions is
      less than 9.5ε for every machine-representable point in the complex plane. Please
      refer to comments in the header files themselves and to the above mentioned
      paper for more information on the implementation methodology.
    </p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
      Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
      Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
      Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
      Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../inverse_complex.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inverse_complex.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="asin.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>
